setting up a probabilistic calculation

oetnewfun('prob_example1_stochast',...
    'output', 'stochast')

Define the stochastic variables within the newly created function. Create a structure with the fields 'Name', 'Distr' and 'Params'. Each stochastic variable must have a name, a distribution and parameters. The distribution functions should have as first input argument the P (probability), the second and possibly following input arguments are the parameters which have to be specified in "Params" (in the right order). The number of stochastic variables can be chosen depending on the system to solve. The definition of the stochast variable can be customised as long as the general structure is preserved. The following lines are optional; these lines allow the user to set (temporary) one or more variables to deterministic without editting in the function itself.

stochast = struct(...
    'Name', {
        'R'... % example stochastic variable "R" (Resistance or Strength)
        'S'... % example stochastic variable "S" (Solicitation or Load)
        },...
    'Distr', {
        @norm_inv... % distribution function (of R)
        @norm_inv... % distribution function (of S)
        },...
    'Params', {
        {8 1}... % mu and sigma (of R)
        {6 1}... % mu and sigma (of S)
        } ...
    );

OPT = struct(...
    'active', true(size(stochast)));

OPT = setproperty(OPT, varargin{:});

for i = find(~OPT.active)
    stochast(i).Distr = @deterministic;
end

The input and output variables as specified here must be used.

oetnewfun('prob_example1_x2z',...
    'output', 'z',...
    'input', {'samples' 'Resistance' 'varargin'})

Define the Z-function in the newly created function. Z must be calculated. This part can be customised, as long as the output "z" is a column vector with the same number of rows as samples.R (or of samples.S, which is the same). In this example, z is easily calculated in one line of code. However, many alternatives are possible. Other functions can be called, or even external programs. Note that in some cases a loop is required to calculate all instances separately.

% calculate z (in this case: Z = R - S)
z = samples.R - samples.S;

After saving both the stochast-function and the x2z-function, the model is ready to run. When calling the FORM routine, it is essential that both the stochast and the x2z-funtion are parsed.

FORMres = FORM(prob_example1_stochast,...
    'x2zFunction', @prob_example1_x2z);

displayFORMresult(FORMres)

plotFORMresult(FORMres)

A similar calculation can be easily carried out with the Monte Carlo method as well.

MCres = MC(prob_example1_stochast,...
    'x2zFunction', @prob_example1_x2z,...
    'NrSamples', 1000);

plotMCResult(MCres,...)
    'space', 'x');